Detailed syllabus by subject for each semester (One detailed sheet per subject) (All fields must be filled in)
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Université Djilali BOUNAAMA Khemis Miliana Faculty of Material Sciences and Computer Science Department of Mathematics 3rd Year Licence Licence Title: Mathematics Academic Year: 2024–2025 |
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جامعة الجيلالي بونعامة خميس مليانة كلية علوم المادة والاعلام الالي قسم الرياضيات السنة الثالثة ليسانس عنوان الليسانس: رياضيات السنة الدراسية :2024-2025
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Detailed syllabus by subject for each semester |
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Semester 6
Teaching Unit: Fundamental Unit /Core Unit
Subject: Partial Differential Equations
Credits: 9
Coefficient: 5
Course Objectives:
An introduction to Partial Differential Equations (PDEs), their associated methods and main issues. The aim is to learn resolution techniques specific to each type of PDE.
Recommended Prerequisites: Analysis, Algebra, Topology
Course Content:
Chapter 1: Elliptic Case
· Separation of variables
· Study of the Dirichlet problem for the Laplacian (n = 2, n = 3)
(Poisson kernel, Green's functions for the ball and the half-plane)
Chapter 2: Hyperbolic Case – Wave Equations
· Solution by separation of variables
· Representation of the solution
· Huygens’ Principle (n = 1, n = 2)
· Vibrating strings and plates (Fourier series)
Chapter 3: Parabolic Case – Heat Equation
· Solution by separation of variables and superposition (Fourier series)
· Solution representation in ℝⁿ and its regularity
· Specific equations (Bernoulli, Riccati, Clairaut)
Assessment Method: Final exam (60%), continuous assessment (40%)
References:
· J. Bass, Mathematical Analysis, Vol. 2
· Hervé Reinhardt, Partial Differential Equations: Course and Solved Exercises